Pseudo-Formal Linearization Method for Nonlinear Systems and Its Application to an Electric Power System

This paper presents a pseudo-formal linearization method based on the polynomial approximation for nonlinear systems. The given nonlinear system which is expressed by the ordinary differential equation is piecewisely linearized with respect to an augmented linearization function which consists of polynomials by the formal linearization approach. Then each linearized system is smoothly united into a single linear one by an automatic choosing function. This method is making use of Taylor expansion as the basis and Chebyshev interpolation as a faster calculation of linearization. As an application of this method, a nonlinear observer is designed to estimate the states of an electric power system. Numerical experiments show the effectiveness of this method.